Question

Can somebody help me to solve this?

Answer 1

B

Explanation:

Given

`√(ab)` =
`√(bc)` ( square both sides )

ab = bc ( divide both sides by b ) , then

a = c

Given

`√(ac)` =
`√(4c^4)` ( square both sides )

ac = 4
`c^(4)` ( but a = c) , so

4
`c^(4)` = c² ( subtract c² from both sides )

4
`c^(4)` - c² = 0 ← factor out c² from each term on the left side

c²(4c² - 1) = 0 ← 4c² - 1 is a difference of squares

c²(2c - 1)(2c + 1) = 0

Equate each factor to zero and solve for x

c² = 0 ⇒ c = 0

2c - 1 = 0 ⇒ 2c = 1 ⇒ c =
`(1)/(2)`

2c + 1 = 0 ⇒ 2c = - 1 ⇒ c = -
`(1)/(2)`

But c > 0 , then c =
`(1)/(2)` → B